The following is a list of chapters and sections in Ideals, Varieties, and Algorithms: An introduction to computational algebraic geometry and commutative algebra, Second Edition, by David Cox, John Little, and Donal O'Shea. If you want to read part of the Introduction, follow this link.
Chapter 1: Geometry, Algebra, and Algorithms
§1.1. Polynomials and Affine Space
§1.2. Affine Varieties
§1.3. Parameterization of Affine Varieties
§1.4. Ideals
§1.5. Polynomials of One Variable
Chapter 2: Groebener Bases
§2.1. Introduction
§2.2. Orderings on the Monomials in k[X1,...,Xn]
§2.3. A Division Algorithm in k[X1,...,Xn]
§2.4. Monomial Ideals and Dickson's Lemma
§2.5. The Hilbert Basis Theorem and Groebner Bases
§2.6. Properties of Groebner Bases
§2.7. Buchberger's Algorithm
§2.8. First Applications of Groebner Bases
§2.9. (optional) Improvements on Buchberger's Algorithm
Chapter 3: Elimination Theory
§3.1. The Elimination and Extension Theorems
§3.2. The Geometry of Elimination
§3.3. Implicitization
§3.4. Singular Points and Envelopes
§3.5. Unique Factorization and Resultants
§3.6. Resultants and the Extension Theorem
Chapter 4: The Algebra-Geometry Dictionary
§4.1. Hilbert's Nullstellensatz
§4.2. Radical Ideals and the Ideal-Variety Correspondence
§4.3. Sums, Products, and Intersections of Ideals
§4.4. Zariski Closure and Quotients of Ideals
§4.5. Irreducible Varieties and Prime Ideals
§4.6. Decomposition of a Variety into Irreducibles
§4.7. (optional) Primary Decomposition of Ideals
§4.8. Summary
Chapter 5: Polynomial and Rational Functions on a Variety
§5.1. Polynomial Mappings
§5.2. Quotients of Polynomial Rings
§5.3. Algorithmic Computations in k[X1,...,Xn]/I
§5.4. The Coordinate Ring of an Affine Variety
§5.5. Rational Functions on a Variety
§5.6. (optional) Proof of the Closure Theorem
Chapter 6: Robotics and Automatic Geometric Theorem Proving
§6.1. Geometric Description of Robots
§6.2. The Forward Kinematic Problem
§6.3. The Inverse Kinematic Problem and Motion Planning
§6.4. Automatic Geometric Theorem Proving
§6.5. Wu's Method
Chapter 7: Invariant Theory of Finite Groups
§7.1. Symmetric Polynomials
§7.2. Finite Matrix Groups and Rings of Invariants
§7.3. Generators for the Ring of Invariants
§7.4. Relations Among Generators and Geometry of Orbits
Chapter 8: Projective Algebraic Geometry
§8.1. The Projective Plane
§8.2. Projective Space and Projective Varieties
§8.3. The Projective Algebra-Geometry Dictionary
§8.4. The Projective Closure of an Affine Variety
§8.5. Projective Elimination Theory
§8.6. The Geometry of Quadric Hypersurfaces
§8.7. Bezout's Theorem
Chapter 9: The Dimension of a Variety
§9.1. The Variety of a Monomial Ideal
§9.2. The Complement of a Monomial Ideal
§9.3. The Hilbert Function and the Dimension of a Variety
§9.4. Elementary Properties of Dimension
§9.5. Dimension and Algebraic Independence
§9.6. Dimension and Nonsingularity
§9.7. The Tangent Cone
Appendix A: Some Concepts from Algebra
§A.1. Fields and Rings
§A.2. Groups
§A.3. Determinants
Appendix B: Pseudocode
§B.1. Inputs, Outputs, Variables, and Constants
§B.2. Assignment Structures
§B.3. Looping Structures
§B.4. Branching Structures
Appendix C: Computer Algebra Systems
§C.1. AXIOM
§C.2. Maple
§C.3. Mathematica
§C.4. REDUCE
§C.5. Other Systems
Appendix D: Independent Projects
§D.1. General Comments
§D.2. Suggested Projects